Neuronal Avalanches: Critical Brain Dynamics

Network State

σ = 1.00 — Critical

Current avalanche

Last avalanche size

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Measured branching ratio

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Avalanches so far

Controls

Branching parameter σ 1.00

External drive rate 0.30%

Refractory period (steps) 2

Steps per second 12

How it works

Each of the ~1,700 neurons sits on a 3D lattice with 6 nearest neighbours (k = 6). When a neuron fires, it independently activates each quiescent neighbour with probability:

p = σ / k

so the expected number of "child" firings
per firing neuron is exactly σ.

This is a branching process — the same mathematics used for nuclear chain reactions and epidemics, applied here to cortical activity (Beggs & Plenz, 2003):

σ < 1 (subcritical) — cascades die out almost immediately; small, exponentially-distributed avalanches.
σ = 1 (critical) — cascades can die or grow with equal likelihood at every step. Avalanche sizes follow a power law P(s) ~ s^-3/2, with no characteristic scale — exactly what Beggs & Plenz measured in cortical slice recordings.
σ > 1 (supercritical) — cascades tend to grow without bound, like runaway seizure-like activity.

A small external drive rate spontaneously fires a random quiescent neuron whenever the network falls silent, so avalanches keep being triggered. Each neuron also has a brief refractory period after firing (it cannot re-fire immediately), matching a real neuron's absolute refractory period after an action potential.

The critical-brain hypothesis proposes that healthy cortex self-organises near σ ≈ 1 because this maximises dynamic range and information transmission across the network — this simulation lets you push the same network away from that point in both directions and watch the qualitative change in dynamics.

Firing neuron Refractory Quiescent

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